1. Field of the Invention
The present invention relates generally to a system and method of application of an artificial neural network to solving an inverse physical problem, whereby an unknown starting condition of a physical process is determined based upon a known ending condition. Such an artificial neural network may be used for various purposes, such as the creation of a die design based upon a metal part specification, in one embodiment.
2. Description of the Prior Art
Among the most difficult problems of modern science and engineering are those requiring for their solutions the computational resources of the world's largest and fastest supercomputers. Typical problems include aerodynamic modeling, weapons modeling, structural modeling, material property modeling at both atomic and molecular scales, material process modeling, weather forecasting, etc.
The computational resources essential for the efficient evaluation of these and similar modeling problems are extremely expensive and are readily accessible at but few of the major National Laboratories and Research Centers. Even in the context of these very powerful computing systems and those anticipated soon to be tens or hundreds of times more powerful still, processing times may exceed days or weeks for problems of relatively modest proportions. The inevitably limited access to such machines severely limits the number of problems that may be addressed. Compounding the issue of limited access is the fact that many, perhaps most, of the problems submitted to these machines for solution are of a very specific nature (for example, material and/or process modeling involving process parameters and material properties of limited ranges). Thus, the solutions obtained are applicable over a usually very limited range in the values of the defining parameters and arc of relatively little utility beyond the specific regimes for which the calculations have been performed. Without question, the results of these modeling studies are very accurate (within the limitations imposed by the underlying theory). Nevertheless, the ensuing "point results" are of little general utility since the broader physical relationships inherent in their development are in no generally applicable manner captured by the numerical results of the modeling programs.
One example of a complex computational problem is that of designing a die for producing a metal part (e.g., a car fender or door). As presently performed, the die design process for a part of any substantive complexity is highly iterative in nature. Moreover, it is a process whose successful execution depends to a very great extent on the acquired art of a limited and diminishing number of human experts. A measure of the difficulty of the die design task and, thus, an estimate of the importance of the new method are suggested by the oft-quoted assertion that reducing by one or two the required number of design iterations for a complex part could save $20 billion dollars per year in the automotive industry alone.
It is important to bear in mind that modern computational methods are quite capable of solving a variation of the die design problem. Thus, if a die configuration Is known, it is possible to compute the configuration of the part that would result from a forming operation involving the die under a specified set of conditions (ram speed, lubrication, hold-down force, et.). Although not trivial, the computations required for the solution of this "forward" problem are well within the capabilities of any contemporary high-end computing system.
The "Inverse" problem, on the other hand, is extremely difficult, if not impossible, to solve generally by conventional mathematical or computational methods, regardless of the computational resources applied. In view of this, a more formal statement of one specific problem addressed by the present patent may be taken as development of a computational method whereby a particular "inverse" problem, production of a die design given a part specification, could be solved using available technologies. A more encompassing definition of the general problem addressed by the present patent would include development of a general computational method whereby previously intractable "inverse" problems from other disciplines could be solved. Examples are found in such diverse areas as metal forging, glass and ceramic production (indeed, material design in general), process control (a nuclear reactor or chemical plant, for instance), traffic flow optimization, and many others.
It should be noted that a variation of the above-described problem, and any solution thereto, is of particular relevance in those process control applications for which the capability to learn not only the operating schema of a complex system but mechanisms for correcting "off-normal" operation of such a system can be of great importance. As applied to the material stamping problem, this capability can be employed to compensate for such inevitable effects as die wear variations in material thickness and material properties, and the like.
The traditional die design process is, as already noted, an iterative one in which a craftsman produces, based on his experience, a "first guess" representation for the die configuration he deems most likely to produce a "target" part in the material required and under the stamping conditions specified. A part is formed using the die (and the associated "tooling") and characterized using one or another form of three-dimensional metrology. Unless the designer is very lucky, this first formed part will deviate substantially from the specified target part. The skilled designer utilizes the deviations to guide his development of a refined die representation. A second die is fabricated and a second part formed and characterized. Very likely, this second part is found to deviate less severely than the first from the target part but not yet to conform to it. Thus, the process is repeated again and again until the worst-case deviations are found to be within some specified tolerance limit. Perhaps a half-dozen iterations, each costing tens of thousands of dollars or more, may be required before a satisfactory die is produced.
As suggested by the highly iterative nature of the traditional die design process, a new die design can require months for its final realization. Related to this time is a considerable cost. It is not unusual for the design process for a relatively simple component to cost $50,000 or more. Both of these considerations carry a considerable burden in a modern industrial setting wherein it is often necessary to design a product as complex as an automobile from scratch and produce a working prototype within one year. There is therefore a significant need in the art for a system and process for solving an "inverse" problem as described above, and more specifically a system for designing dies for metal stamping.